Water Properties
Water Conductivity & Dielectric Properties
Water's electrical properties—conductivity and dielectric constant—directly affect WFC performance in VIC circuits. Understanding these properties helps predict circuit behavior and optimize design.
Dielectric Constant of Water
Water has an exceptionally high dielectric constant due to its polar molecular structure:
Relative Permittivity (εr):
| Pure water at 20°C: | εr ≈ 80 |
| Pure water at 25°C: | εr ≈ 78.5 |
| Pure water at 100°C: | εr ≈ 55 |
Temperature Dependence:
εr(T) ≈ 87.74 - 0.40 × T(°C)
Why Water's εr is High
Water molecules are polar (have positive and negative ends). In an electric field, they align with the field, effectively multiplying the field's ability to store charge. This is why water-based capacitors have such high capacitance per unit volume.
Comparison with Other Materials
| Material | εr | Relative Capacitance |
|---|---|---|
| Vacuum/Air | 1 | 1× (reference) |
| PTFE (Teflon) | 2.1 | 2.1× |
| Glass | 4-10 | 4-10× |
| Ceramic | 10-1000 | 10-1000× |
| Water | 80 | 80× |
Water Conductivity
Conductivity measures how easily current flows through water:
Conductivity (σ) Units:
- Siemens per meter (S/m)
- Microsiemens per centimeter (µS/cm) - most common
- Millisiemens per centimeter (mS/cm)
1 S/m = 10,000 µS/cm = 10 mS/cm
Resistivity (ρ = 1/σ):
ρ (Ω·cm) = 1,000,000 / σ (µS/cm)
Conductivity of Different Waters
| Water Type | σ (µS/cm) | ρ (Ω·cm) | Source |
|---|---|---|---|
| Ultra-pure (Type I) | 0.055 | 18,000,000 | Lab grade |
| Deionized | 0.1-5 | 200,000-10,000,000 | DI systems |
| Distilled | 1-10 | 100,000-1,000,000 | Distillation |
| Rain water | 5-30 | 33,000-200,000 | Natural |
| Tap water (typical) | 200-800 | 1,250-5,000 | Municipal |
| Well water | 300-1500 | 670-3,300 | Ground water |
| Sea water | 50,000 | 20 | Ocean |
| 0.1M NaOH | ~20,000 | ~50 | Electrolyte |
Calculating Solution Resistance
For Parallel Plates:
Rsol = ρ × d / A = d / (σ × A)
Example:
- Tap water: σ = 500 µS/cm = 0.05 S/m
- Electrode area: 100 cm² = 0.01 m²
- Gap: 2 mm = 0.002 m
- Rsol = 0.002 / (0.05 × 0.01) = 4 Ω
Effect on Q Factor
Solution resistance directly impacts circuit Q:
Qtotal = 2πfL / (Rchoke + Rsol + Rother)
Example Impact:
| Water Type | Rsol | Q (if Rchoke=5Ω) |
|---|---|---|
| Distilled (σ=5 µS/cm) | ~400 Ω | Q ≈ 1.5 |
| Tap (σ=500 µS/cm) | ~4 Ω | Q ≈ 70 |
| Electrolyte (σ=20000 µS/cm) | ~0.1 Ω | Q ≈ 125 |
Insight: Very pure water has high Q losses! For VIC resonance, moderate conductivity may be optimal.
Frequency Dependence
Both εr and σ vary with frequency:
| Frequency | εr Effect | σ Effect |
|---|---|---|
| DC - 1 MHz | Constant (~80) | Constant (DC value) |
| 1 MHz - 1 GHz | Begins to decrease | May increase |
| >1 GHz | Decreases significantly | High dielectric loss |
For VIC frequencies (1-100 kHz), these effects are negligible.
Temperature Effects Summary
- εr: Decreases ~0.4% per °C (capacitance drops as water heats)
- σ: Increases ~2% per °C (resistance drops as water heats)
- Net effect: Resonant frequency increases slightly with temperature
Measuring Water Properties
Conductivity Meters:
- TDS meters (approximate, assume NaCl)
- True conductivity meters (more accurate)
- Laboratory grade (calibrated, temperature compensated)
DIY Measurement:
- Use known electrode geometry cell
- Measure AC resistance at 1 kHz (to avoid polarization)
- Calculate σ from geometry and resistance
VIC Matrix Calculator: Enter water conductivity in the Water Profile section. The calculator computes solution resistance and shows its impact on circuit Q. Temperature compensation is also available.
Next: Calculating WFC Capacitance →